News, Housing Boom-Bust Cycles, and Monetary Policy Birol Kanik and Wei Xiao y October 11, 2009 Abstract In this paper, we explore the possibility that a housing market boom-bust cycle may arise when public beliefs are driven by news shocks. News, imperfect and noisy by nature, may generate expectations that are overly optimistic or pessimistic. Over-optimism easily leads to excessive buildup of housing assets, and creates a housing boom that is not based on fundamentals. When the news is found false or inaccurate, investors revert their actions, and a downturn in the housing market follows. By altering agents net worth conditions, a housing cycle can have signi cant repercussions in the aggregate economy. In this paper, we construct a dynamic general equilibrium model that can give rise to a news-driven cycle, and we then explore what types of monetary policies are appropriate in terms of stabilizing it. JEL classi cation: E3, E4, E5 Keywords: business cycle; news; monetary policy. Department of Economics, State University of New York at Binghamton, Binghamton, NY 13902. bkanik1@binghamton.edu y Department of Economics, State University of New York at Binghamton, Binghamton, NY 13902. wxiao@binghamton.edu Email: Email:
1 Introduction The notion that excessive public expectations can cause housing market booms and busts is now widely accepted by policymakers and the public. Recent research has successfully incorporated housing sectors into dynamic general equilibrium models, but typically does not consider expectation errors as an independent source of uctuations. This paper explores the idea that noisy signals or news can generate optimism and pessimism in agent expectations, which in turn a ect housing demand. When the news is found inaccurate, the subsequent adjustment in expectations and reversal in asset transactions complete a boom-bust cycle. An important feature of the model is that housing assets serve as collateral for credit-constrained agents. By altering the borrowers net worth conditions, a housing cycle can have signi cant repercussions in the aggregate economy. This mechanism is consistent with the so-called credit view, that asset market conditions are not merely re ections of economic conditions, but also a cause of uctuations. Until recently, credit channels are often absent from dynamic general equilibrium models. Bernanke and Gertler (1989) and Williamson (1987) provide the earlier works that consider nancial intermediation and agency costs as propagation mechanisms for aggregate shocks in dynamic general equilibrium models. 1 Kiyotaki and Moore (1997) make important progress by examining the role of credit constrained agents and collateralized debts on equilibrium output. Bernanke et. al. (1999) embed a nancial accelerator in a sticky price environment, and make monetary policy analysis possible. Finally, recent works, such as those by Iacoviello (2005) and Monacelli (2009), speci cally incorporate a housing sector into general equilibrium models with collateral constraint, and examine monetary policy s proper response to housing market uctuations. 2 The development of the literature naturally leads to a debate on policy issues. Since Bernanke et. al. (2001) posed the question should central banks respond to asset prices?, it has become an important area of dialogue. Most research suggests that it is not necessary for in ation-targeting and Taylor rule regimes to respond to asset prices, on the ground that asset price movements 1 Carlstrom and Fuerst (1997) build on Bernanke and Gertler (1989), and evaluate the e ect of agency cost quantitatively. 2 Other quantitative works in this area include Calza et. al. (2007) and Pariès and Notarpietro (2008). 1
tend to change output gaps and in ation in the same direction, which can be taken care of by the regime (Batini and Nelson, 2000; Bernanke and Gertler, 2001; Iacoviello, 2005). Some research, however, nds that targeting asset misalignment in addition to in ation and output gaps does improve economic stability (Ceccetti, et. al., 2000). The debate between Bernanke and Gertler (2001) and Ceccetti et. al. (2000) is especially instructional. They both use the Bernanke and Gertler model to search for optimal interest rate rules, but draw distinct conclusions. What makes the di erence is that in Bernanke and Gertler (2001), the economy is subject to both fundamental and non-fundamental shocks, and the central bank cannot distinguish them, whereas in Ceccetti et. al. (2000), the only shock is non-fundamental, and the central bank is aware of the price misalignment. 3 A critical lesson from this debate is that one cannot view the relationship between asset prices and in ation/output as a stylized fact; it depends on the underlying sources of uncertainty. In this paper, we propose that a source of uncertainty - news shocks - is important for the housing market in particular, and for the aggregate economy in general. It is important because news, imperfect and noisy by nature, may generate expectations that are overly optimistic or pessimistic. Over-optimism easily leads to excessive buildup of housing assets by investors, and creates a housing boom that are not based on fundamentals. When the news is found false or inaccurate, investors revert their actions, and a downturn in the housing market follows. This explanation of a housing boom-bust cycle is inspired by the insight of Cochrane (1994), Beaudry and Portier (2004) and Jaimovich and Rebelo (forthcoming). In their works, noisy news about technological progress is an important source of business cycles. This type of cycles are referred to as Pigou cycles since the idea dates back to the earlier works of Pigou in 1926. Our interests in this view of the cycle were also motivated by a salient fact of the recent U.S. housing market. Real housing prices signi cantly deviated from economic fundamentals during the 1998-2007 episode of housing boom (Shiller, 2007). In Figure 1, we reproduce with newer data a graph from Shiller (2007), which shows that real housing prices surpassed real rental prices and 3 In one experiment Bernanke and Gertler consider a single non-fundamental shock, and nd that adding an asset price target is better than pure in ation targeting. However, they emphasize that asset prices can be substituted by output gaps. 2
200 Real Owners Eqivalent Rent Case Shiller Real Home Price Index 180 Turner Building Cost Index 160 140 120 100 80 1985 1990 1995 2000 2005 2010 Figure 1: Housing price, construction cost, and owner s equivalent rent real building costs between 1998 and 2007. Case and Shiller (2003) s survey results further show that speculative psychology played major roles in homeowners purchasing decisions during much of the housing boom. These facts suggest that one needs to look beyond traditional fundamentals for plausible explanations of the recent housing cycle, and we believe the Pigouian explanation is one such candidate. Based on Iacoviello (2005), we construct a general equilibrium model in which credit-constrained borrowers use their housing assets as collateral to nance their purchases. Optimistic news raises these agents expected future net worth, expands their borrowing capacity, and allows them to purchase more housing and consumption goods. Higher housing demand raises housing prices and creates a housing boom. The housing boom further increases the borrowing agents net worth, and raises their purchases even more. Aggregate demand therefore increases, driving work hours and output up, producing an economic expansion. The opposite works for pessimistic news. This is the major transmission mechanism of the model. We show that when there is incorrect optimistic news about future demand, this transmission mechanism creates a housing boom and comovement among 3
aggregate variables, and when the true shock is revealed, the adjustment in expectations generates a sharp decline in housing prices. A recession then follows. A major di culty with the news-driven business cycle literature is that it is very hard to generate comovement among aggregate variables. In a real business cycle model, for example, positive news about future productivity changes has a strong wealth e ect. It makes economic agents go on vacation consume more, work less and produce less, and invest less to pay for the higher consumption. Good news creates a recession instead of a boom. Beaudry and Portier (2004) generate positive comovement with a multi-sector economy in which investment decisions and consumption decisions are decoupled so that the substitution between the two due to the wealth e ect can be minimized. In Jaimovich and Rebelo (forthcoming), adjustment cost, capacity utilization, and preferences that incorporate a weak wealth e ect on labor supply are used to generate positive comovement. Christiano et. al. (2008) study a sticky wage model with a monetary authority that targets in ation. When there is positive productivity news, the central bank s policy can keep in ation and real wages from rising too quickly, so that unemployment and production losses can be prevented. This helps generate positive comovement among economic aggregates. In this paper, we rely on two features of the model to generate comovement. One is the nature of the shock. The driving force of our model is a demand shock a shock to housing preferences. Unlike an expected productivity shock, news about future demand does not have a wealth e ect on all agents and all sectors of the economy. The other is the credit channel. When housing price rises, improved net worth relaxes the borrowing constraint, stimulates aggregate demand and generate an economic boom along with a housing boom. Equipped with a working model, we proceed to ask what monetary policies are appropriate in dealing with news-driven business cycles. We consider Taylor-type interest rules. We nd that the impact of a housing boom-bust cycle does depend on the interest rate policy. If the policy s reaction to the boom is too weak, the impact of the housing cycle on the aggregate economy is large. Finally, we ask whether or not a strong policy reaction entails a speci c housing price target in the interest rate rule. An interest rate rule is deemed best if it minimizes the central bank s loss function. We 4
consider scenarios in which news shocks are mostly noisy, and ones in which they are mostly correct. We also distinguish between cases where uncertainty comes from news about housing demand, and those where news about productivity changes is the major impulse. We run stochastic simulations to search for an optimal policy rule. Our result suggests that the gain from targeting asset prices, in addition to output and in ation, is minimal, if any. The conclusion is reminiscent of Bernanke and Gertler (2001) and similar works. Our contribution to this area of research is therefore to con rm that targeting asset prices is unimportant even when business cycles are mainly driven by optimistic and pessimistic expectations. The rest of the paper is organized as follows. Section 2 lays out the micro-founded model framework and derives the equilibrium conditions. Section 3 explores whether or not news-driven cycles can arise in this model. Section 4 presents the policy analysis. Section 5 concludes. 2 A benchmark model The model is based on Iacoviello (2005), Bernanke et. al. (1999) and Kiyotaki and Moore (1997). Consider a discrete time, in nite horizon economy where a patient household (lender), an impatient household (borrower), a wholesaler rm, and some retailers reside. The borrower is less patient than the lender because she discounts the future more heavily. Both households consume, work and demand a housing asset. The borrower uses her housing asset as a collateral to borrow from the lender, and her capacity to borrow is limited by the expected future value of her discounted asset holdings. The wholesaler hires labor from both households to produce a homogeneous intermediate good. There are a large number of monopolistically competitive retailers who buy the intermediate good and di erentiate it into consumption goods, and sell to the households. As in Bernanke et. al. (1999), the retailers are Calvo-type price setters that are the source of sticky prices. Collateralized borrowing, adopted from Iacoviello (2005), provides the critical channel via which changes in net worth a ects the aggregate economy. 5
2.1 Patient household/lender The lender maximizes a lifetime utility function given by: X 1 E 0 t=0 t 1(ln C 1t + d t ln h 1t L 1t ); subject to the constraint C 1t + q t h 1t + R t 1b 1t 1 t = b 1t + q t h 1t 1 + w 1t L 1t + F t ; (1) where E 0 is the expectation operator, 1 is the discount factor, C 1t is consumption, h 1t is her holding of housing asset, and L 1t is hours worked. b t = Bt P t represents real holdings of one period loan, R t 1 is the nominal interest rate, q t = Qt P t is real housing price, w 1t = W1t P t is real wage, t = Pt P t 1 is in ation rate, and F t represents real pro ts received from the retailers. P t is the general price level at time t. The variable d t is a preference shock that shifts the marginal rate of substitution between housing and consumption/leisure. Note that all capital letters represent the nominal counterparts of the de ned real variables, and the subscript 1 is used to tag all variables of the patient household. The subscript 2 will shortly be used to denote variables of the impatient household. Note that by putting total housing stock into the utility function, we implicitly assume that housing services are proportional to the housing stock. This is a fairly standard household problem that can be solved to yield the following rst order conditions 1 w 1t = L 1 1t ; C 1t (2) q t = d t q t+1 + C 1t h 1 E t ; 1t C 1t+1 (3) 1 R t = C 1 E t : 1t t+1 C 1t+1 (4) 6
2.2 Impatient household/borrower The impatient household s problem is similar to that of the patient household, except for two di erences. First, the impatient household does not own any retailers and does not receive pro ts, and second, her borrowing capacity is constrained by the discounted future value of the collateral - her housing assets. The problem thus is max E 0 1 X t=0 t 2(ln C 2t + d t ln h 2t L 2t ); subject to C 2t + q t h 2t + R t 1b 2t 1 t = b 2t + q t h 2t 1 + w t L 2t ; (5) b 2t m 2 E t ( q t+1h 2t t+1 R t ): (6) A requirement of 2 < 1 ensures that this household is more impatient than the lender and will need to borrow from her. The amount that the debtor can borrow, in nominal terms, is bounded by m 2 E t ( Qt+1h2t R t ); where 0 < m 2 < 1. In other words, a fraction 1 m 2 of the housing value cannot be used as collateral. One can broadly think of 1 m 2 as the down payment rate, or think of m 2 as the loan-to-value ratio. As shown in Iacoviello (2005), this setup ensures that the borrowing constraint will always be binding in the steady state. Solving this problem yields the following conditions: 1 w 2t = L 1 2t ; C 2t (7) q t = d t q t+1 + C 2t h 2 E t + t E t m 2 t+1 q t+1 ; 2t C 2t+1 (8) 1 R t = C 2 E t + t R t ; 2t t+1 C 2t+1 (9) where t is the Lagrangian multiplier associated with the borrowing constraint. 7
2.3 Intermediate goods rm The intermediate goods (wholesaler) rm hires labor from both households as inputs to produce a homogeneous good Y t : Y t = L 1tL 1 2t ; (10) where 0 < < 1. After the intermediate goods are produced, retailers purchase them at the wholesale price P w t, and transform them into nal goods and sell them at the price P t. We denote the markup of nal over intermediate goods as X t = Pt P w t The producer maximizes her pro t. Y t =X t w 1t L 1t w 2t L 2t : (11) subject to (10). 2.4 Retailers There are a continuum of retailers indexed by i. Retailer i buys the intermediate good in a competitive market, di erentiates it at no cost into Y t (i); and sells it at P t (i). Total nal goods are aggregated from each individual nal good as Y f t = [ Z 1 0 Y t (i) " 1 " di] " " 1 ; (12) where " > 1. Each retailer s demand curve is Y t (i) = [ P t(i) P t ] " Y f t : (13) The price index of nal goods is P t = [ Z 1 0 P t (i) 1 1 " di] 1 " : (14) 8
We assume Calvo-type pricing for retailers. Each retailer can only change the price with probability 1. The optimal pricing decision is max P o t 1X k C 1t E t f 1 [ P t o C 1t+k k=0 P t+k P w t+k Y t+k (i)]g subject to (13). P o t represents the optimal price chosen by the retailer to maximize the objective. The retailers use the lender s discount factor because they are owned by her. Di erentiating with respect to P o t implies that the optimal set price must satisfy: 1X k E t f k C 1t 1 [ P t o (i) C 1t+k k=0 P t+k X X t+k )Y t+k (i)]g = 0: (15) Given that the fraction of retailers do not change their price in period t, the aggregate price evolves according to P t = [P 1 " t 1 o1 " + (1 )P 1 " : (16) t ] 1 These two conditions can be combined to create the new Phillips curve in the linearized version of the model. Finally, we assume there is a central bank that implements a Taylor-type interest rate rule that targets the current levels of output gap, in ation, and housing price. The speci c rule will be spelled out later. 2.5 Equilibrium The equilibrium of the model is a sequence of prices {q t ; R t ; P t ; X t; w 1t ; w 2t ;}, and an allocation {h 1t ; h 2t ; L 1t ; L 2t ; Y t ; C 1t ; C 2t ; b 1t ; b 2t ;}, such that all rst order conditions and constraints hold, and all markets clear. 9
Goods market clear when 4 C 1t + C 2t = Y t : (17) It is straightforward to show that the retailer pro t is equal to F t = X t 1 X t Y t : (18) The loans market equilibrium is b 1t + b 2t = 0: (19) As in Iacoviello (2005), housing assets are assumed to have a xed total supply H, which leads to the trivial market clearing condition h 1t + h 2t = H: (20) With a xed total supply and no production required, the variable h is essentially the land variable of Kiyotaki and Moore (1997). It seems that a more realistic modelling of housing units should require the combination of land and a housing structure that is produced with labor and materials. Davis and Heathcote (2005), for example, take this latter approach to model housing in a real business cycle model. Is our approach too simplistic? The answer depends on how much generality is lost for our purpose. Between 1975 and 2006, the real price of residential land in the U.S. rose 270%, while the real price of housing structures only rose for about 33% (Davis and Heathcote, 2007). In other words, most of the housing price boom has been a land price boom. Our model does capture this most important element of housing dynamics, and the abstraction from reality allows us to proceed with much less cumbersome mathematics. 5 After obtaining the equilibrium, we linearize the model s critical equations around the steady state. We use lower-case letters to denote linearized variables. 4 As in Iacoviello (2005), total output can be approximated by Y f t = R 1 0 Yt(i)di Yt. 5 In reality there are unoccupied land that can be added to total land supply. But as research shows, the amount of unoccupied land near residential areas is limted. This plus land-use regulations have made land supply relatively inelastic (Mishkin, 2007). 10
2.6 Transmission mechanism Collateralized borrowing has a signi cant impact on the monetary transmission mechanism. To see this, consider how the interest rate policy a ects the user cost of capital (housing) for lenders and borrowers, respectively. De ne the user cost of capital as the marginal rate of substitution between housing and consumption U h =U c. It measures how many units of consumption goods an agent is willing to give up in exchange for a unit of housing, and can be viewed as the unit price of the housing asset in terms of consumption goods. The intuition is more transparent when we consider linearized versions of the Euler equations. For lenders, the Euler equations (3) and (4) can be combined to de ne the user cost as user cost = 1 1 1 q t 1 1 1 E t q t+1 + 1 1 1 r t = q t 1 1 1 (E t q t+1 q t ) + 1 1 1 r t : (21) Monetary policy (changes in nominal rates) a ects user cost via two conventional channels: one, by raising or lowering the real interest rate r t, de ned as i t E t t+1 ; and two, by causing uctuations in current and future housing prices. In particular, expected monetary tightening lowers the expected housing appreciation (second term on the right-hand-side), and raises current cost of capital. Note that we assume there is no depreciation for housing assets. For the borrowers, the collateral constraint adds another channel via which monetary policy can a ect user cost. Linearize (8) and (9) to obtain u.cost 1 1 e q t e 1 e E t q t+1 + 1 1 e r t + (1 m 2)( 1 2 ) 1 e t : (22) The two conventional channels are covered by the rst three terms, which are similar to those in (21). The last term in (22) is the key. t is the Lagrangian multiplier for the collateral borrowing constraint (30). It measures the shadow price of borrowing the marginal bene ts of increasing the value of the collateral by one more unit, which relaxes the borrowing constraint and allows the agent to purchase more consumption and housing to improve welfare (see8). When t = 0, the collateral 11
constraint is not binding, and the agent is not credit-constrained. The higher the value of t, the tighter the collateral constraint. The tighter the collateral constraint, the more valuable an extra unit of housing asset is since it can relax the constraint, and the more consumption goods agents are willing to give up to obtain it, and therefore the higher the user cost. For credit-constrained borrowers, monetary policy a ects user costs by tightening or relaxing the borrower s collateral constraint. For example, higher nominal rates lower the value of the collateral housing asset by discounting it more heavily and by lowering its expected future price. This tightens the borrowing constraint and raises user costs. In essence, tighter monetary policy reduces housing demand by worsening the balance sheet of the borrowers. This is the critical credit channel that is absent in a conventional model with unrestricted borrowing. The credit channel generates interesting dynamics in the housing market. When the nominal rate goes down (so does the real rate), for instance, the user cost of capital decreases for both the lender and the borrower. However, the borrower s user cost decreases more than the lender s due to the extra credit channel. Given a xed housing supply, the borrower s holding of housing assets will go up while the lender s will go down. Figure 2: Response of housing price and borrower s housing assets to an expansionary policy shock 12
In gure 2, we plot the impulse responses of housing price and borrower s housing to an unexpected expansionary interest rate shock. We assume the central bank s policy is simply i t = t + e R t ; e R t = R e R t 1 + t ; where 0 < R < 1 and t is a shock with mean 0 and standard deviation. We let = 1:2 ( > 1 is required to obtain a unique rational expectations solution) and R = 0:75. We assume the policy shock is 1% in size. On impact, housing price increases by 0.3%, and borrower s housing assets increase for as much as 12%. Since there is a xed housing supply, the lender s holdings of housing assets must have gone down. The credit channel also enhances the impact of the interest rate policy on aggregate economic activities a point well made by Kiyotaki and Moore (1997) and Iacoviello (2005). High housing values increase the net worth of the borrowers, and allow them to borrow more and spend more; more aggregate demand increases total output and spending, and further increases housing prices and the net worth. This nancial accelerator e ect is absent when there is no collateralized borrowing. In gure 3, we plot the response of output to an expansionary interest rate shock with and without the collateral constraint. The diagram depicts the strength of the credit channel that we just describe. 6 3 News driven business cycles 3.1 The basic mechanism Next we investigate qualitatively whether or not economic news can generate boom-bust housing and business cycles. A natural question to ask is what type of information is contained in the news. Most research in this area favors news about future productivity changes. In Beaudry and Portier (2004 and 2007), 6 The plot with no credit channel is obtained by simulating a version of the model where there is no collateral constraint, and the two agents are equally patient. 13
Figure 3: Response of output to an exansionary monetary shock with and without borrowing constraints for example, it is news about productivity that drives a Pigou cycle. While this type of news is very appropriate in explaining episodes such as the boom of the late 1990s, we believe it is not the best impulse mechanism to consider for our model. We are trying to understand a housing boom-bust cycle driven by expectations. As Case and Shiller (2003) s survey reveals, a big motive behind buyers housing rush was the perception of rapid and steady future price increases, which led to but were also con rmed (self-ful lled) by steady increase in demand. Buyers actual income or perceived income did not necessarily rise. When productivity news is the main source of cycles, it is the optimism about future income and permanent wealth that raises aggregate demand. That mechanism does not seem to match our situation here. 7 So we consider a di erent type of news news about future housing preferences. To be precise, it is news about the variable d t in the utility function, a rise of which would increase the marginal rate of substitution of housing services against consumption and leisure. An advantage of this approach is that d t is by de nition a demand-side shock; a rise in it would indicate stronger preferences by agents to own housing assets. Moreover, higher demand naturally leads to higher housing prices. Optimistic news about future housing demand can be thought of as optimistic news about higher prices. In fact, if we linearize the housing 7 Higher future housing prices certainly increase buyers expected future wealth, but this increase is not related to productivity growth. 14
price equation (3), we obtain q t = ( 1 1)h 1t + c 1t + 1 E t (q t+1 c t+1 ) + (1 1 )d t : When d t rises, the housing price variable q t will shift upward. In other words, d t is essentially a shock to housing prices. Positive news about future d t is positive news about future housing prices. We de ne a realistic news-driven boom-bust cycle as one that meets two conditions: (1) positive news rst leads to a boom de ned as an increase in housing prices, aggregate output, employment, and consumption, and (2) the realization that news is too optimistic leads to a recession de ned as a fall in the same set of variables. The comovement of housing prices and aggregate variables is key to a news-driven cycle. A major di culty with the news-driven cycle literature is that in a typical general equilibrium model, it is very hard to generate comovement among aggregate variables. For instance, in a real business cycle model, positive news about future productivity changes has a strong wealth e ect. It makes economic agents go on vacation consume more, work less and produce less, and invest less to pay for the higher consumption. Good news creates a recession instead of a boom. In order for plausible comovement to arise, researchers often need to consider more re ned and sophisticated economic environment. Beaudry and Portier (2004) generate positive comovement with a multisector economy in which investment decisions and consumption decisions are decoupled so that the substitution between the two due to the wealth e ect can be minimized. In Jaimovich and Rebelo (forthcoming), adjustment cost, capacity utilization, and preferences that incorporate a weak wealth e ect on labor supply are used to generate positive comovement. Christiano et. al. (2008) study a sticky wage model with a monetary authority that targets in ation. When there is positive productivity news, the central bank s policy can keep in ation and real wages from rising too quickly, so that unemployment and production losses can be prevented. This helps generate positive comovement among economic aggregates. In this paper, we rely on two features of the model to generate comovement. One is the nature of the shock. Unlike an expected productivity shock, an expected demand shock does not have a 15
wealth e ect on all agents and all sectors of the economy. The other is the credit channel. When housing price rises, improved net worth should stimulate aggregate demand and generate positive comovement among aggregate variables. We demonstrate this point next. But before we proceed, we need to calibrate the model s parameters. The discount factor is set at 0.99 for the lender and 0.98 for the more impatient borrower. The elasticity of substitution across intermediate goods, ", is set a 4, a value commonly used in the literature. The inverse of the elasticity of labor supply,, is set to 1.01, as in Iacoviello (2005), which makes the labor supply curve virtually at. The fraction of rms that keep their prices unchanged,, is given a value of 0.75, which corresponds to an average price duration of about one year. The steady state value of the preference shock, d t, is set at 0.1. The share of the lender s labor in the production,, is set at 0.5. The borrower s downpayment rate, 1 m 2, is given a value of 0.1. For a benchmark experiment, we assume the central bank implements a simple in ation targeting rule i t = 1:2 t : The dynamics we derive with more complicated policy rules are similar to the ones we show here. Finally, we assume the fundamental shock d t follows an AR(1) process d t = d d t 1 + e d t ; where e d t is a random shock with mean 0 and variances 2 d. For our benchmark simulation, we assume d = 0:95. There is a news shock t that arrives several periods before the true shock e d t is revealed. The timing of the news shock is as follows. At time zero the economy is in the steady state. At time one, unanticipated news arrives. For example, agents might learn that there will be a one-percent increase in e d t after p periods. In period p + 1, the actual shock to e d t is revealed. If the news is accurate, e d t will be exactly equal to the value suggested by the news in period one. But if the news is inaccurate, e d t can be any value that di ers from the news. In our experiment, we let e d t to be 16
zero in the inaccurate news scenario, so that without the incorrect news, the economy would have stayed in the original steady state. Also, we set the number of periods between the arrival of news and the realization of shocks p to be 6. If p is too small, we will not be able to observe any economic dynamics between time 0 and p. If p is too large, the predictive horizon of the news seems too long to be realistic. We pick p = 6 somewhat arbitrarily to satisfy these two criteria. The techniques that we use in this section and next are closely related to the papers that we reference, such as those of Christiano, et. al. (2008). In gure 4, we plot the impulse response of output/consumption and housing price to news about a 1% future increase in e d t. The news is accurate. In gure 9 in the appendix, we show the impulse response functions of more variables such as in ation, total borrowing, total borrower housing, and total labor hours. Although the actual preference shock takes place in period seven, agents learn about it in period one. Agents react to this news by re-optimizing their objectives. Consequently, we see in gure 4 consumption and output increase, and so do housing prices. From gure 9 in the appendix, we can see that the borrower has increased her housing asset and collateralized borrowing, which via the credit channel has contributed to the increased aggregate demand. In period seven, when the actual preference shock is realized, the economy is already on its convergent path back to the steady state. Since the news is accurate, the realization of the shock does not bring any new information, and therefore does not alter the agents newly optimized plan (in period one) for consumption, housing, and output. How does a news shock generate comovement among housing prices, consumption, labor hours and output? A closer look at gure 9 reveals what happens when the positive news arrives. Both the borrower and the lender now have a stronger urge to hold and consume housing assets, but they cannot both hold more because the supply of housing assets is xed. Since more housing assets provide the borrower with extra bene ts a relaxed borrowing constraint and the ability to borrow and spend more, the borrower is more willing to pay for the increased housing price. So the borrower s housing assets increase, and the lender s decrease. Higher housing price and more housing assets allow the borrower to borrow more, consume more, and work less. The lender, on 17
Figure 4: Impulse response of output and housing price to correct news about housing demand the other hand, must consume less to lend more to the borrower. This extra saving is justi ed by the rising nominal and real interest rate. Finally, the lender must work more to compensate for her loss of consumption and housing assets. The increase in the lender s labor hours more than o sets the decrease in the borrower s. Hence total hours and total production rise. Next we consider the scenario where the news shock is exactly incorrect. In period one, agents learn about a 1% increase in the preference shock e d t. But in period seven, they observe that there is no preference shock at all. We plot the impulse responses in gure 5 and 10 in the appendix. Upon receiving the news and believing it is accurate, agents reactions are identical to those in gure 2. In period seven, however, the actual shock is realized and the agents learn that the new has been incorrect. They immediately re-optimize their objectives by incorporating the new information. There are sharp decreases in output, consumption, labor, housing prices, and the borrower s housing assets and total debts. Between period one and seven, almost all variables have experienced a cycle that is shaped like an inverted U. Moreover, output/consumption went below its steady state value for a considerable amount of time, creating an prolonged recession. The type of dynamics in gure 5 is what we would like to characterize as a news-driven boombust cycle. What is particularly interesting is that throughout the whole episode, there has been no change in fundamental shocks at all. The only change has been some incorrect news that altered agents expectations between period one and seven. As in Beaudry and Portier (2004), we can de ne 18
Figure 5: Impulse response of output and housing price to incorrect news about housing demand optimism as the case where agents expectations are better than reality. Then what gure 5 shows is exactly a case where optimism alone can generate a boom-bust cycle. Indeed, since such a cycle is clearly not fundamental-based, one is tempted to call the temporary housing price hike in gure 5 a bubble. 3.2 Extensions A noticeable feature of gure 4 and 5 is that given a 1% news shock, the responses in output and housing prices are small in sizes. Housing prices, for example, only increase for about 0.2% at the peak of the response function. This implies that large demand shocks or news about demand shocks are required to generate any signi cant uctuations in the housing market and in the aggregate economy. We believe the simplicity of our model is largely responsible for this result. In a model with richer dynamics and a stronger credit channel, the response of aggregate variables to news shocks should be stronger. We proceed to extend our model next. We note that another important reason for considering these extensions is that when we search for an optimal monetary policy (next section), the quantitative results do matter. We need a more realistic model. We add two new features to the benchmark model. The rst feature is that the housing asset or land becomes a factor of production, so that the intermediate goods producer must also engage in trading in the housing market; the second feature is that the intermediate goods producer is 19
Figure 6: Response to a news shock in the extended model now credit-constrained, and must borrow collateralized loans. We call this version of the model the extended model. We list the details of the extension in the appendix. In gure 6, we plot the impulse response of output/consumption and housing price to a 1% (accurate) news shock in the extended model. As we can see, the response of output/consumption is about 1.5%, while the response of housing price is about 0.45%. Both responses are much stronger than in the benchmark model. In gure 11 in the appendix, we plot the impulse responses of a more complete set of variables for this simulation. Overall, the responses of all variables have increased in magnitude, indicating that the dynamics of the model have been enhanced with the extension. The model has hitherto been free of any physical capital, which is obviously empirically implausible. An important feature of news-driven cycles is the positive response of investment to optimistic news. In our last version of the model, we build on the extended model and add physical capital. More speci cally, we let the intermediate goods producer to be able to make investment decisions and accumulate physical capital, which is now an input for production. We also add adjustment 20
Figure 7: Response to a news shock in the full model cost to capital and to housing assets. We call this version the full model. 8 In the appendix, we write down full details of these models and list all the calibrated parameters. In gure 7, we plot the impulse response of output and housing price to a 1% (accurate) news shock in the full model. This time not only the response of output remains strong, the response of housing price also catches up. On impact the responses of both are about 1.5%. In gure 12 in the appendix, we plot the impulse responses of a more complete set of variables for this simulation. As we expected, on impact of the positive news, there is comovement between investment and housing prices, along with consumption, labor hours, and output. 8 The full model becomes identical to the quantitative model developed and estimated by Iacoviello (2005). 21
4 News shock and monetary policy 4.1 Alternative policy rules and the real impact of news How should the central bank respond to a news-driven housing cycle? Are keeping the interest rate too low responsible for the size of the housing bubble? In previous simulations, we have assumed a very simple in ation-targeting monetary regime. In this section, we examine what impact the central bank s policy rule has on the size of the housing boom and bust cycles. We are interested in Taylor-type policy rules that target in ation, output and possibly housing prices: i t = E t t + y y t + q q t : (23) As a rst experiment, we simply consider four alternative policy rules and examine the model s impulse responses to a news shock under each rule. The four rules are: rule one : i t = 1:2 t ; (24) rule two : i t = 2:2 t ; (25) rule three : i t = 2:2 t + 0:5y t ; (26) rule four : i t = 2:2 t + 0:5y t + 0:5q t : (27) (24) is the benchmark policy rule that we use for the previous section. Since the reaction parameter to in ation must be bigger than 1 for the model to have a unique equilibrium, we use this rule to represent a regime that responds to in ation relatively weakly. 9 We use (25) to represent a rule that responds to in ation strongly. (3) is a conventional Taylor rule that not only targets in ation, but also targets output gaps. Finally, (27) is a Taylor rule that, in addition to in ation and output targeting, also targets housing prices. We plot the impulse responses of output and housing prices in the full model in gure 8. Three 9 With this rule, the nominal rate responds more than one-for-one to in ation, and therefore satis es the Taylor principle and quali es as an active policy. In this sense our reference to it as a weaker policy is only true when our basis of comparison is a stronger rule like 25. 22
features are worth noting. One, when pure in ation-targeting is the policy rule, the policy reaction parameter does not seem to make too big a di erence as far as the responses of output and housing prices are concerned. Under the rst rule (weak targeting) and the second rule (strong targeting), the responses of output and housing prices are both strong, and the sizes do not vary much when the policy rule changes. Two, the Taylor rule is a much better stabilization tool than the pure in ationtargeting rule. With rule three, the responses of both output and housing prices are dampened compared with the previous two rules. In particular, output s response decreases for as much as 50% on impact of the initial shock. Three, when asset price is added as a policy target, both the responses of output and housing prices are substantially dampened. But the response seems to overreact and forces output to go below trend for a prolonged period of time. If measured in volatility, it is unclear whether or not this rule is more stabilizing or not. Figure 8 makes it clear that monetary policies indeed matter for the impact of the housing boom. Comparing the output responses under rule one and rule three, for example, reveals that if the monetary authority keeps the interest rate relatively low (rule one), the housing market boom would cause a much larger output boom than with higher interest rate (rule three). 4.2 Should the central bank respond to housing prices? A natural question to ask is whether or not central banks can better stabilize the economy by speci cally targeting housing prices, in addition to output gaps and in ation. Such conclusions cannot be drawn by examining impulse response diagrams. We turn to stochastic simulations for some quantitative answers. We assume that the central bank s loss function comprises the volatility of two variables output gaps and in ation. 10 The central bank s goal is to pick policy parameters ; y and q to minimize an weighted average of the unconditional standard deviation of the two variables. In our experiments, we allow to vary between 1.01 and 3 (again, > 1 ensures a determinate, unique equilibrium), y to vary between 0 and 2, and q to vary between 0 and 1. These restrictions are put in place to ensure 10 To be more precise, y t and t measure the percentage deviations of the two variables from their long-run steady state values. 23
Figure 8: Impact of alternative policy rules on the response to news shock that the policy parameters are within a (generous) range consistent with empirical estimates. For each variation of the policy rule, we run stochastic simulations of the model to calculate the central bank s loss function. The optimal policy parameters are the ones that minimize this function. For each variation of the policy rule, we consider three di erent calibrations of the news shock. In the rst calibration, the news shock is always an accurate prediction of the fundamental shock. In the second calibration, the news shock is positively correlated with the fundamental shock. The news is wrong sometimes, but on average it does help agents make a better forecast. In the third calibration, the news is completely noisy it is uncorrelated with the fundamental shock and provides no useful information for forecasting. We expect no surprise from the rst case. Since the news is always correct, it is essentially a situation where all shocks are anticipated. The policy prescription should not be very di erent from the case where shocks are observed when they are realized. What might become interesting are the latter two cases where the level of noises in the news increases. We run our policy experiments for the benchmark model and report the results in table 1. We 24
Signal quality Optimal policy parameters ( ; y ; q ) min(0:25 + 0:75 y ) min( + y ) min(0:75 + 0:25 y ) Accurate news 3:05; 2; 0:1 3:05; 0:9; 0 3:05; 0:5; 0 Corr(news,fund.shock) = 0:5 3:05; 2; 0:05 3:05; 1:1; 0 3:05; 0:8; 0 Noisy news 3:05; 2; 0:15 3:05; 0:8; 0 3:05; 0:5; 0 Table 1: Optimal policy parameters:benchmark model consider three possible weight allocations for the central bank s loss function. We use 0:25 +0:75 y to represent a loss function that emphasizes output stabilization, 0:75 + 0:25 y to represent one that emphasizes in ation stabilization, and a third one that puts equal weights on output and in ation. The results suggest that the interest rate policy should strongly target in ation, especially when there is more weight on in ation volatility in the loss function; that it should target the output gap, especially when there is more weight on output volatility in the loss function; and that its response to housing prices should be very small, if any. In fact a small response to housing prices is found bene cial only in one case, where the central bank puts a heavy weight on output stabilization and a small weight on price stability. What is striking is that the optimal policy reaction function seems to be una ected by the quality of news. For example, the suggested optimal policy reaction is strong for in ation, and is weak for housing prices across all three weight allocations and all three calibrations for news shocks. Most of the experiments suggest zero or near-zero policy reaction for housing prices, with the exception of one case (column 1 of table 1), where the largest policy response parameter for housing prices is 0.15, representing a 1.5 percent increase in the nominal interest rate when housing prices rise by 10%. Tables 2 shows our simulation results for the extended model. The results suggest an optimal policy that is very similar to that in Table 1. The optimal response to in ation remains strong in nearly all cases, and the optimal response to housing prices continue to be weak. In fact this time the highest policy reaction parameter for housing prices is only 0.05, as opposed to 0.15 in the benchmark model. A major di erence between the benchmark model and the extended model is that the latter has a stronger credit channel, which is probably why the optimal response to output 25
Signal quality Optimal policy parameters ( ; y ; q ) min(0:25 + 0:75 y ) min( + y ) min(0:75 + 0:25 y ) Accurate news 1:05; 2; 0:05 2:65; 2; 0:05 3:05; 0:3; 0 Corr(news,fund.shock) = 0:5 1:05; 2; 0:05 2:25; 2; 0:05 3:05; 0:9; 0 Noisy news 1:05; 2; 0:05 2:75; 2; 0:05 3:05; 0:8; 0 Table 2: Optimal policy parameters:extended model Optimal policy parameters ( ; y ; q ) Signal quality min(0:25 + 0:75 y ) min( + y ) min(0:75 + 0:25 y ) Accurate news 1:05; 2; 0:05 1:05; 2; 0:05 3:05; 1; 0 Corr(news,fund.shock) = 0:5 1:05; 2; 0:05 1:05; 2; 0:05 3:05; 1:5; 0 Noisy news 1:05; 2; 0:05 1:05; 2; 0:05 3:05; 0:6; 0 Table 3: Optimal policy parameters:full model is now higher across all cases. We report the results for the full models in tables 3. The full model is the most empirically plausible version that not only has a strong credit channel as in the extended model, but also accounts for investment dynamics in the real economy. It turns out that the calculated optimal policy parameters bear very similar characteristics with those suggested by the benchmark and extended models: strong response to in ation, positive response to output in most cases, and very weak response to housing prices. The results suggest that the interest rate policy should strongly target output when stabilizing output gaps has high weights in the central bank s loss function. Another experiment we run but do not report here is the case where the target t is replaced with E t t+1 in the policy rule. This turns the policy into a forward-looking rule. All the simulation results under that rule are very similar to those in table 1-3. The conclusion that responding to asset prices is unimportant is reminiscent of the ndings of Bernanke and Gertler (2001) (for general asset prices) and Iacoviello (2005). The purpose of our experiment is to investigate whether or not the existing conclusions need to be modi ed when business cycles are driven by news. Our result suggests that these conclusions continue to prevail. 5 Conclusion We explore the possibility that a housing boom-bust cycle can be driven by news in a dynamic general equilibrium model with collateral constraint. We nd that news about housing demand can 26
generate housing boom-bust cycles. Housing values a ect agents net worth and their ability to borrow and spend. A housing cycle can therefore trigger similar movements in aggregate economic activities. When economic news is inaccurate, most of the uctuations are not based on fundamentals and are later canceled by the realization of the real shocks. This kind of uctuations have the feature of bubbles. We nd that if the central bank s response to the housing cycles is weak, the impact of the cycle on the real economy is large. We ask the question how should central bank respond to news-driven cycles? To answer the question, we ran stochastic simulations of the model economy, and look for the optimal interest rate policy that minimizes the central bank s loss functions. Our results suggest that the central bank should target in ation and output gaps, and need not target housing prices. References [1] Batini, N. and E. Nelson 2000, When the Bubble Bursts: Monetary Policy Rules and Foreign Exchange Market Behavior, working paper, Bank of England. [2] Beaudry P. and F. Portier 2004, An Exploration into Pigou s Theory of Cycles, Journal of Monetary Economics 51, 1183-1216. [3] Beaudry, P. and F. Portier 2007, When can changes in expectations cause business cycle uctuations in neoclassical settings?, Journal of Economic Theory, 135 (1), 458-477. [4] Bernanke, B. and M. Gertler 1989, Agency Costs, Net Worth, and Business Fluctuations, American Economic Review 79 (1), 14-31. [5] Bernanke, B. and M. Gertler 2001, Should Central Banks Respond to Movements in Asset Prices? American Economic Review 91 (2), 253-257. 27